Why do you get 24 volts on my HVAC air handler when the fuse is out and 7 volts when the fuse is put back in?

You are reading the voltage across the fuse holder and getting a back reading from another piece of control equipment that is using a common return. The reading should be taken from a common ground or neutral point to one side of the fuse holder. You should be looking for the circuit voltage value and then from the other side of the fuse holder to ascertain that the fuse has not blown.